Self Test 5 - Finite span wings Flashcards
Why was an elliptic planform for a wing considered to be advantageous?
An elliptic spanwise lift distribution yields the minimum induced drag. In the absence of either geometric or aerodynamic twist, an elliptic distribution of lift requires an elliptic spanwise variation of chord length, and so the elliptic planform can yield a minimum induced drag.
What is geometric twist in the context of a finite wing and explain the benefit and challenge it represents.
Geometric twist is when the angle of attack of the aerofoil section (i.e. angle of the chordline) varies with spanwise position. The purpose is to achieve a spanwise lift distribution which will minimize induced drag (e.g. by having an elliptic distribution of circulation). However, it means that the structure must be constructed with a twist which can be difficult with metal airframes.
Explain why birds flying in a V-formation is advantageous.
The benefit of flying in a “V” formation is that the trailing tip vortices from two adjacent birds or aircraft can overlap. As these vortice are counter rotating and comparable strength (as the weight of each bird/aircraft is similar the lift will be similar) they will effectively cancel each other. Thus, the downwash effect is significantly reduced. As a result there is less induced drag and so less power is required. However, the leading bird (or aircraft) in the formation will still experience a downwash, while trailing positions in the formation will experience an upwash. So not all positions in the V formation experience the same benefit.
State Helmholz’s third theorem that governs vortex filaments and explain the consequence for flow around a wing of finite span.
Correct
In the absence of external rotational forces, a fluid that is initially irrotational remains irrotational. The corollary is that if the circulation around a defined set of fluid particles is initially zero, it will remain zero.
Therefore, when a wing starts from rest in quiescent fluid (i.e. with zero lift and hence zero circulation) the total circulation in the fluid must remain zero if the flow is irrotational (i.e. dissipation of vorticity due to viscosity is ignored). This means that to balance the circulation on the wing associated with lift, there must be an equally strong but opposite sign circulation shed from the trailing edge. This is the starting vortex. As It does not move with the wing (or in a body fixed frame, it is convected downstream), the effect of this starting vortex will reduce over time, and so for steady conditions can be ignored.
What are the limitations of the Prandtl lifting line theory for 3D wings (i.e. stacked horse vortices)?
The lifting line theory does not account for either viscous flow or swept wings. In addition, it assumes that the vorticity sheet that is shed behind the wing stays planar. This is easily demonstrated to be incorrect for two reasons: firstly the sheet rolls up into a single wing tip vortex on each side; secondly, these two wing tip vortices induce a strong downwards velocity in each other, and so the trailing vortices are below the wing, not in the same plane.
How are Helmolz’ theorems for the motion of vortex filaments satisfied for a 2D aerfoil?
A 2D slice of a vortex filament is a point vortex. For a 2D flow in the x-y plane, any vortex filaments must be parallel to the z axis. Therefore, Helmholz’s first and second theorems are automatically satisfied as the filaments have constant strength and extend to +/- infinity in the z direction. The third theorem is satisfied if no point vortices are removed or allowed to change strength over time. This is satisfied if the flow is inviscid.
State Helmhotz’s first two theorems governing vortex filaments and explain the consequence for flow around a wing of finite span.
1) The strength of a vortex filament is constant along its entire length.
2) A vortex filament connat end at a point in the fluid - it must extend to teh boundaries or form a closed loop.
The consequence is that a lifting wing will generate wing tip vortices which extend downstream towards infinity.
What is aerodynamic twist in the context of a finite span wing and explain the purpose of this feature.
Selected Answer:
[None Given]
Aerodynamic twist is when the shape (especially the camber) of the aerofoil section varies with spanwise position. The purpose is to achieve a spanwise lift distribution which will minimize induced drag (e.g. by having an elliptic distribution of circulation) or to help avoid stall on specific parts of the wing.
